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A comparison of the results of four computer search-models for production planning Many production managers are faced with the problem of planning production, inventory and workforce under the constraint of limited resources to meet a seasonal demand. Considerable research has been done on this planning problem and various models have been proposed. The linear decision rule (LDR), especially as applied to the well-known Paint Shop, represents a milestone in the development of such models and serves as a standard against which the performances of many other models are measured. In this paper a comparison is made between the LDR results and that of three computer search models, SDR, CONMIN and SUMT for the Paint Shop. Two different cost structures are used for the Paint Shop - the original structure developed by Holt et al. (a quadratic approximation to the costs of the Shop) and a ficticious fourth-order cost structure published by Goodman. The results of this study indicate that in cases where the cost structure is non-linear, the computer search techniques can be of some help to the production planner.

In this paper a linear programming (LP) model for aggregate production planning is given. This is a general model that can be used in various production situations. It optimizes the monthly planning of human resources, production quantities and inventories on the medium term (e.g. a 12 month planning horizon) for a multi-department, multi-product production facility. A computer programme was developed for the model, making use of a standard LP package. In practical applications savings of up to 33% of variable cost were obtained.In hierdie artikel word 'n lineere programmeringsmodel (LP) vir aggregaat-produksiebeplanning gegee. Dit is 'n algemene model wat in 'n verskeidenheid van produksiesituasies gebruik kan word. Dit optimiseer die maandelikse beplanning van mannekrag, produksiehoeveelhede, en voorrade op die mediumtermyn (bv. 'n beplanningshorison van 12 maande) vir 'n multi-departementele, multi-produk-produksiefasiliteit. 'n Rekenaarprogram is vir die model ontwikkel, wat van 'n standaard LP-pakket gebruik maak. In praktiese toepassings is besparings van tot 33% van veranderlike koste verkry.

Many production managers are faced with the problem of planning production, inventory and work-force under the constraint of limited resources to meet a seasonal demand. Considerable research has been done on this planning problem and various planning models have been introduced. In those cases where linearity of the cost functions of an undertaking may reasonably be assumed, an ordinary linear programming model suffices. In many cases, however, this simple linear approach to certain essentially non-linear cost functions is unacceptable owing to the gross approximation made.Separable programming (SEP) is introduced as a solution methodology to this aggregate production planning problem in a complex, high-order cost structure case. The cost structure was used by Goodman for the application of goal programming (GP) in this field. The Goodman GP model makes provision for positive or negative slack for the production level, work-force level and inventory level with penalty costs for these slack-deviations. Goodman also made use of a 'sectioning search' model for this high-order cost case to serve as a measure for his GP model. A comparison is made between the results of these three approaches. SEP offered an improvement of more than 4% in total cost in comparison with the sectioning search model, and performs 26% better than the GP model.

In this paper a comparison is made between the results and the cost-effectiveness of two computer search models for aggregate production planning when applied to a very sensitive high-order cost structure. The Search Decision Rule (SOR) model developed by Taubert outperforms the Sectioning Search Model (SECT) of Goodman in both the areas of total optimum cost and cost-effectiveness.